Quantum magic quantifies the resources beyond Clifford operations required for universal quantum computing. 

Here, we study the Pauli spectrum of typical many-qubit states that arise in quantum circuits or as eigenstates of chaotic Hamiltonians. This distribution unveils the structural properties of magic and allows one to compute magic measures such as the stabilizer entropy. 

After presenting a phenomenological picture of the Pauli spectrum based on quantum typicality, we derive the exact Pauli spectrum of Haar distributed states and their stabilizer entropy. 

Building on these findings, we introduce the filtered stabilizer R\'enyi entropy, a measure of magic suitable to discriminate generic many-body states from atypical quantum states, such as product states or ground states of local Hamiltonians.

Our results provide insights into the challenging costs of preparing typical states in digital quantum devices and an alternative characterization of ergodicity for many-body systems.
 

The Zoom registration link:
https://zoom.us/meeting/register/tJAscuihpzkoHte_0z9pjpQw-H6kK829662v